Description Usage Arguments Value Author(s) References See Also Examples
The function calculates the price of a plain vanilla American put with Least Squares Monte Carlo method with Control Variates (Glasserman, 2004). Black & Scholes solution for European put is used as the control. The regression model included in the algorithm is quadratic polynomial (Longstaff & Schwartz, 2000).
1 2 3 4 5 6 7 |
Spot |
Spot price of the underlying asset (e.g. stock). |
sigma |
Volatility of the underlying asset. |
n |
Number of paths simulated. |
m |
Number of time steps in the simulation. |
Strike |
Strike price of the option. |
r |
Interest rate of the numeraire currency (e.g. EUR). |
dr |
Dividend rate of the underlying asset. |
mT |
Maturity time (years). |
x |
An object returned by the functions |
object |
An object returned by the function |
... |
Not used. |
The function returns an object of the class AmerPutCV that is a list comprising the price calculated and the entry parameters. Class-specific print
function gives the option type information and the price. The price as a single number can be derived using the price
function. An overview of the entire object can be seen using the summary
function.
Mikhail A. Beketov
Glasserman, P. 2004. Monte Carlo Methods in Financial Engineering. Springer.
Longstaff, F.A., and E.S. Schwartz. 2000. Valuing american option by simulation: A simple least-squared approach. The Review of Financial Studies. 14:113-147.
Functions: price
,
AmerPutLSM
,
AmerPutLSM_AV
,
AsianAmerPutLSM
, and
QuantoAmerPutLSM
.
1 2 3 4 5 6 | AmerPutLSM_CV()
put<-AmerPutLSM_CV(Spot=14.2, Strike=16.5, n=200, m=50)
put
summary(put)
price(put)
put$price
|
Loading required package: mvtnorm
Loading required package: fBasics
Loading required package: timeDate
Loading required package: timeSeries
American Put Option
Price: 0.1200031American Put Option
Price: 2.431704
American Put Option
Method: Least Squares Monte Carlo with Control Variates
(B&S solution for European Put is used as a control)
Option price 2.431704
Spot price 14.2
Strike 16.5
Volatility 0.2
Number of paths 200
Number of time-steps 50
Interest rate 0.06
Dividend rate 0
Maturity time 1
[1] 2.431704
[1] 2.431704
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